FBX vertex weight import problem
To solve this:


Delete all vertex groups of the mesh. To do this select the mesh then go to the vertex groups panel inside the Object tab and delete all groups as shown below:





Select your mesh first then select your armature as well using shift+ Mouse Right Click
Hit Ctrl+p then choose With Automatic Weights as shown below:





Your mesh will be parented properly with the armature with correct deformation as shown below:




Updated .blend file can be found here: